# How do you verify the identity: #[sin(x) / csc(x) - 1 ] = [ sin (x) + 1 / cot^2 (x) ]#?

##### 1 Answer

Short answer: there is no identity. Here is the logic.

Firstly, it's always advisable to determine the domain of the functions on both sides of the equation.

On the left the restriction is

On the right we need:

Since

Before going any further, it makes sense to check if the identity is true for some simple case. Let's say,

In this case

Therefore, the left side evaluates to

The right side evaluates to

Obviously, these two expressions are not equal to each other for this particular value of